I’ve heard it mentioned many times: Riker would be a captain on any other ship, but since he’s on “The Enterprise”, he’s only the first officer.
So imagine you are Riker, as #1 on the flagship of the fleet. Picard becomes “indisposed” for whatever reason. You are as good as any captain, but not on the Enterprise. Starfleet decides to assign another temporary captain, instead of using Riker, who already knows the ship/crew/etc.
I know I’d be pissed, no matter who the temporary captain was. I’d feel slighted.
Now image you are Jellico. An accomplished captain (who very well could have been the normal captain on the Enterprise), who may or may not be assigned to a ship. Picard becomes “indisposed” for whatever reason. Starfleet decides to assign you as temporary captain of the flaship of the fleet. It’s truly an honor to be chosen to that position. You don’t know the ship, or the crew, very well, so are an outsider. An upstart #1 (who is NOT a captain) feels he should be in command. I’d feel unappreciated/slighted as well.
Looking from either position, I can totally understand Riker and Jellico not liking each other, to say nothing of different command styles. Both have a good claim to acting captain, and neither are particularly wrong.
As another crew member on the Enterprise, who would you like to see as temporary captain?